I would imagine it depends on how strong the digestive acids were etc.. im sure theres birds which pass some seeds through.
Birds' stomachs are evolved into gizzards, gastric mills. Pigeons, chickens, turkeys & other birds intentionally ingest gravel & small stones that their gizzards use to grind up their food with the addition of stomach acids. Their "teeth" are in their stomachs. They also have a crop where food is stored prior to digestion, so the flow of food into the gizzard can be well regulated & the effect very efficient. Damned little gets through intact. I'm sure that varies by species.
http://en.wikipedia.org/wiki/Gizzard#Birds
http://en.wikipedia.org/wiki/Crop_(anatomy)
My brother & I kept racing pigeons & birmingham rollers all through our teens, made it our science project more than once, so I remember some of it, anyway. I scraped plenty of pigeon poop out of nesting boxes, too.